This didn't work. Upon reboot the packages I had previously installed were inaccessible. The files in the root directory were saved, as well as the additional user I had created, but LibreOffice and VLC were greyed out in the menu and would not start.

The kernel line of the menu of the bootloader must have home=/dev/sdxx of the flash drive for persistance to work. If there are other sata drives connected to the computer the flash drive will be the last to be enumerated by udev.

If you need more assistance provide this info:

How did you install slitaz to flash drive:
Applications/System Tools/Create a LiveUSB ?tazusb gen-liveusb ?tazusb gen-iso2usb ?
If not:
What tool did you use to install slitaz on the flash drive ?
What bootloader does it use ?